# Continued Fractions: Continued Fraction, Pell's Equation, Mathematical Constants, Möbius Transformation, Generalized Continued Fraction, Incomplete Gamma Function, Gauss's Continued Fraction, Padé Table, Stern-Brocot Tree, Silver Ratio

General Books, Sep 4, 2011 - Mathematics - 52 pages
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 50. Chapters: Continued fraction, Pell's equation, Mathematical constants, M bius transformation, Generalized continued fraction, Incomplete gamma function, Gauss's continued fraction, Pad table, Stern-Brocot tree, Silver ratio, Minkowski's question mark function, Solving quadratic equations with continued fractions, Convergence problem, Periodic continued fraction, Khinchin's constant, Gauss-Kuzmin-Wirsing operator, Pad approximant, Engel expansion, Euler's continued fraction formula, Complete quotient, Restricted partial quotients, Rogers-Ramanujan continued fraction, Gauss-Kuzmin distribution, Convergent, Stieltjes transformation, Fundamental recurrence formulas, Chain sequence, L vy's constant, Lochs' theorem. Excerpt: In geometry, a M bius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad ? bc ? 0. M bius transformations are named in honor of August Ferdinand M bius, although they are also called homographic transformations, linear fractional transformations, or fractional linear transformations. M bius transformations are defined on the extended complex plane (i.e. the complex plane augmented by the point at infinity): This extended complex plane can be thought of as a sphere, the Riemann sphere, or as the complex projective line. Every M bius transformation is a bijective conformal map of the Riemann sphere to itself. Indeed, every such map is by necessity a M bius transformation. The set of all M bius transformations forms a group under composition called the M bius group. It is the automorphism group of the Riemann sphere (when considered as a Riemann surface) and is sometimes denoted .The M bius group is isomorphic to the group of orientation-preserving isometries of hyperbolic 3-space and therefore plays an impo...

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